- : unit = ()
- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] minus(x,0) -> x
[2] minus(s(x),s(y)) -> minus(x,y)
[3] f(0) -> s(0)
[4] f(s(x)) -> minus(s(x),g(f(x)))
[5] g(0) -> 0
[6] g(s(x)) -> minus(s(x),f(g(x)))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_f(s(x)) , Marked_minus(s(x),g(f(x)))>
<Marked_f(s(x)) , Marked_g(f(x))>
<Marked_f(s(x)) , Marked_f(x)>
<Marked_g(s(x)) , Marked_minus(s(x),f(g(x)))>
<Marked_g(s(x)) , Marked_f(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_f(g(x))>
  <Marked_g(s(x)) , Marked_f(g(x))> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_g(s(x)) , Marked_f(g(x))> --> <Marked_f(s(x)) , Marked_g(f(x))>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_g(f(x))>
  <Marked_f(s(x)) , Marked_g(f(x))> --> <Marked_g(s(x)) , Marked_g(x)>
  <Marked_f(s(x)) , Marked_g(f(x))> --> <Marked_g(s(x)) , Marked_f(g(x))>
}

{  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  f(0) >= s(0) ;
  f(s(x)) >= minus(s(x),g(f(x))) ;
  g(0) >= 0 ;
  g(s(x)) >= minus(s(x),f(g(x))) ;
  Marked_g(s(x)) >= Marked_g(x) ;
  Marked_g(s(x)) >= Marked_f(g(x)) ;
  Marked_f(s(x)) >= Marked_g(f(x)) ;
  Marked_f(s(x)) >= Marked_f(x) ;
 }
 + Disjunctions:{ 
{
  Marked_g(s(x)) > Marked_g(x) ;
 }
{
  Marked_g(s(x)) > Marked_f(g(x)) ;
 }
{
  Marked_f(s(x)) > Marked_g(f(x)) ;
 }
{
  Marked_f(s(x)) > Marked_f(x) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: f(0) >= s(0)
constraint: f(s(x)) >= minus(s(x),g(f(x)))
constraint: g(0) >= 0
constraint: g(s(x)) >= minus(s(x),f(g(x)))
constraint: Marked_g(s(x)) >= Marked_g(x)
constraint: Marked_g(s(x)) >= Marked_f(g(x))
constraint: Marked_f(s(x)) >= Marked_g(f(x))
constraint: Marked_f(s(x)) >= Marked_f(x)
APPLY CRITERIA (Subterm criterion)

ST: Marked_minus -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] minus(x,0) -> x
[2] minus(s(x),s(y)) -> minus(x,y)
[3] f(0) -> s(0)
[4] f(s(x)) -> minus(s(x),g(f(x)))
[5] g(0) -> 0
[6] g(s(x)) -> minus(s(x),f(g(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_f(s(x)) , Marked_minus(s(x),g(f(x)))>
<Marked_f(s(x)) , Marked_g(f(x))>
<Marked_f(s(x)) , Marked_f(x)>
<Marked_g(s(x)) , Marked_minus(s(x),f(g(x)))>
<Marked_g(s(x)) , Marked_f(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(x)) , Marked_g(f(x))>
<Marked_f(s(x)) , Marked_f(x)>
<Marked_g(s(x)) , Marked_f(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 1*X0 + 0; 
 [ g ] (X0) = 1*X0 + 0; 
 [ s ] (X0) = 3 + 3*X0 + 0; 
 [ 0 ] () = 0; 
 [ Marked_g ] (X0) = 3 + 1*X0 + 0; 
 [ f ] (X0) = 3 + 3*X0 + 0; 
 [ Marked_f ] (X0) = 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.037372 seconds (real time)
Cime Exit Status: 0